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Preheat the oven to 400 F. Line cookie sheet with parchment paper or silicone mat.
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To make the dough, combine the butter, oil and brown sugar. Mix for a couple minutes until it is smooth and fluffy. Add the egg and vanilla and mix again. Add the remaining ingredients and mix until just combined.
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To make the streusel, combine all the ingredients in a bowl and mix with a spoon or your hand. Start with 1/3 cup of flour. The mixture should stick together, but should also crumble when you run it through your fingers. If it isn't crumbling, add 1 tbsp additions of flour until it crumbles.
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Using a large (1/4 cup) cookie scoop, scoop a ball of dough onto a lined baking sheet. Using the back of your cookie scoop or your fingers, make an indent on the top of the dough. Sprinkle a couple tablespoons of the streusel on the top of the cookie, into the indent.
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Bake the cookies at 400 for 9-11 minutes. Cool on wire racks.
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To make the icing, combine the powdered sugar, milk, and vanilla in a small bowl and whisk until it's smooth and runny. Drizzle on cooled cookies.
